In a typical mixer for receiving two different bands, a mixed frequency (mixing frequency) fs is selected as follows:fs≈(f1+f2)/2,  (1)wherein f1 is the center frequency of a first signal to be received, and f2 is the center frequency of a second signal to be received.
In this case, the intermediate frequency fIF is as follows:fIF≈|f1−f2|2  (2)and the bandwidth BIF is as follows:BIF=max(B1,B2),  (3)wherein B1 is the bandwidth of the first signal to be received, and B2 is the bandwidth of the second signal to be received.
This minimizes the bandwidth of the signal that may be used (for a single downconversion mixer). On the one hand, in the case of a sampling mixer, a low-pass filter is easy to implement, on the other hand, this low-pass filter may allow the intermediate frequency fIF to pass. This would be disadvantageous for the filter performance (for example an attenuation within the stop band). Additionally, in a sampling mixer, an order of an IIR filter of the sampling mixer is typically limited to one, so that with a given bandwidth, there is no freedom in terms of filter design.
In summary, in a sampling receiver, a capacitance for low-pass filtering is typically used following the sampling mixer so as to prevent aliasing in the subsequent decimation process. If two bands are to be received simultaneously with one single downconversion (downmixing) operation, the intermediate frequency will typically be placed to be halfway between the two bands.